SOLUTION: If a bicycle wheel makes 7 rotations a second and has a diameter of 75cm, what cosine function describes the height of a point on the edge of the wheel ?

Question 1199690: If a bicycle wheel makes 7 rotations a second and has a diameter of 75cm, what cosine function describes the height of a point on the edge of the wheel ?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Let the height be at a maximum at t=0. A point on the rim will oscillate about
the wheel axis, which is at the center of the circle of diameter 75 cm. The
height at t=0 will be 75. The equation describing the height is:
h(t) = A(1 + cos(wt)), where A = the amplitude of oscillation and w = the angular frequency.
At t=0, cos(wt) = 1 which gives the initial height of 75. After a half rotation,
the cos(wt) = -1, which gives a height of 0 as expected.
If the wheel makes 7 revolutions per second, w = 7 rev/s*2pi rad/rev = 14*pi/s.
Thus, the equation is h(t) = 37.5(1 + cos(14*pi*t))
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